The idea behind gaze interaction using Pursuits is to leverage the human's smooth pursuit eye movements performed when following moving targets. However, humans can also anticipate where a moving target would reappear if it temporarily hides from their view. In this work, we investigate how well users can select targets using Pursuits in cases where the target's trajectory is partially invisible (HiddenPursuits): e.g., can users select a moving target that temporarily hides behind another object? Although HiddenPursuits was not studied in the context of interaction before, understanding how well users can perform HiddenPursuits presents numerous opportunities, particularly for small interfaces where a target's trajectory can cover area outside of the screen. We found that users can still select targets quickly via Pursuits even if their trajectory is up to 50% hidden, and at the expense of longer selection times when the hidden portion is larger. We discuss how gaze-based interfaces can leverage HiddenPursuits for an improved user experience.